
% Author: Kazuma Takakura
% Date: 17 May 2025
% Time: 10:50:36

\begin{table}[h!]\footnotesize
  \centering
  \caption{Long-term Effects}
\label{tab:robust}
\scalebox{0.7}{
\begin{threeparttable}
\begin{tabular}{lccccccc}\toprule
  & PSM^a & IPWRA^a & AIPW^a & Lee Bound & Lee Bound & Lee Bound & Lee Bound  \\
  &  &  &   & (Lower) & (Upper) &  (Lower, Tight)^b & (Upper, Tight)^b \\\midrule\midrule
  Rapid math test score & -0.223  & -0.266** & -0.266** & -0.664*** & 0.261* & -0.613*** & 0.230  \\ 
    & ( XXX ) & (0.125) & (0.126) & (0.197) & (0.154) & (0.220) & (0.183) \\ 
  RSES score & 0.534*** & 0.502***  & 0.499*** & -0.059 & 0.810*** & 0.052 & 0.783***  \\ 
     & ( XXX ) & (0.175) & (0.174) & (0.204) & (0.176) & (0.199) & (0.206) \\ 
  CPCS score & 0.583*** & 0.527***  & 0.525*** & -0.008 & 0.840*** & 0.065 & 0.816***  \\ 
    & ( XXX ) & (0.169) & (0.168) & (0.190) & (0.171) & (0.201) & (0.179) \\ 
\midrule
\end{tabular}
\begin{tablenotes}
\item (a) For estimating the propensity score function and the outcome model, we use covariates including student's grade, sex, baseline cognitive and baseline non-cognitive score, DT baseline time, branch dummy (location), parents' income source, last income per family member, number of household members, age of household head, education level of household head, teacher's age, teacher's sex, and phone survey dummy.
\item (c) Standard errors are reported within parentheses. For propensity score matching estimation, we calculate clustered bootstrap standard errors based on \cite{otsu2017bootstrap}. For IPWRA and AIPW, we calculate clustered standard errors. For Lee bounds estimation, we calculate bootstrap standard errors.
\item (d) The numbers of observations are as follows:243 for rapid math test score and 236 for RSES and CPCS in PSM, IPWRA, and AIPW. 1005 for rapid math test score and 998 for RSES and CPCS in Lee bounds. 
\item (e) $^*$ Significant at 10\% level; $^{**}$ significant at 5\% level; $^{***}$ significant at 1\% level. 
\end{tablenotes}
\end{threeparttable}
}
\end{table}




